Given $ m \angle ABC = 9x - 100$, $ m \angle CBD = 8x + 26$, and $ m \angle ABD = 147$, find $m\angle CBD$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {9x - 100} + {8x + 26} = {147}$ Combine like terms: $ 17x - 74 = 147$ Add $74$ to both sides: $ 17x = 221$ Divide both sides by $17$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle CBD$ $ m\angle CBD = 8({13}) + 26$ Simplify: $ {m\angle CBD = 104 + 26}$ So ${m\angle CBD = 130}$.